[kayaker]

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in the above case how often would you lay down your pair of jacks?

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Depending on stack sizes and my read on the opponent, I may play that for another card. In that case you figure your outs from the flush/straight and add your possible outs to a set or two pair (must be a Q, as another A coming on the board will not help you). So that's 6 more outs on each street for an extra ~13% on each street, ~26% total.

Then also keep in mind that you hitting a Q MAY make Broadway for your opponent.

Once you have all of that factored in, and you give yourself odds (ranging from ~40% down to ~15%), figure the odds that a) hitting your hand will in fact win, b) you actually have the best hand right now and c) you can get your opponent to fold a better hand through aggressive betting. If you look at the best end of it and you have ~40% to win and you think you can meet one of the other scenarios more than 60% of the time, you should play. If you consider the bottom end, you'd have to make one of the scenarios more than 85% of the time - a much more difficult proposition.

Of course this is a little simplified and does not take pot odds into consideration. Yes, it's a complex process and I do not claim to understand all of the angles that must be considered. This is why it's strongly recommended that beginners throw a hand like this away most of the time. If anything, consider it as second pair and ignore the back-door draws until/unless you hit a card on the turn.